Math Is Fun Forum

EMPhillips1989

Member

Registered: 2008-01-21

Posts: 40

discrete maths

I've been studying prime numbers but have got stuck on the following question, any suggestions would be much appreciated!!!

if p is prime, use al-Haytham to prove that
    (p-2)!=1 mod p

I've looked at the proof when for (p-1)! but i havent been able to see how to adapt the proof to this question please help!!!

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: discrete maths

I dont know much about congruence
I looked up the al-Haytham theorm on Wiki
(p-1)! = -1 (mod p)

knowing that  (p-2)!(p-1) = -1 (mod p)
(p-1) = -1 (mod p)

Thus (p-2)! =1 (mod p)

I am not sure if its correct lol